Please assist with practice problems and provide explanations,

3. Let Y1, Y2, ..., Yo be a random sample from N(0, 1) and let Y10 be another independent random variable from N(0, 1). Let Y = -Zi=, Y, and U = Xi=,(Y, - Y)2. What is the distribution of? a) Y; b) U; c) T = Xi1 Y?; d) V = U+ Yjo e) W = 4- 9Y +Y10 U6. (Level of difculty for this problem may be higher than others) Let Y1 and Y2 be random variables having the joint probability density function 8.702: 0$y151.05y251, yigyz f0'1a3'2) = 0, otherwise Let U = Yl. Y2 a) Find the cumulative distribution function of U; b) Using the cumulative distribution function of U derived in (a) above, nd the probability density function of U. Hence find lMU)